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As the pixel resolution of imaging equipment has grown larger, the images’ sizes and the number of pixels used to represent objects in images have increased accordingly, exposing an issue when dealing with larger images using the traditional deep learning models and methods, as they typically employ mechanisms such as increasing the models’ depth, which, while suitable for applications that have to be spatially invariant, such as image classification, causes issues for applications that relies on the location of the different features within the images such as object localization and change detection. This paper proposes an adaptive convolutional kernels layer (AKL) as an architecture that adjusts dynamically to images’ sizes in order to extract comparable spectral information from images of different sizes, improving the features’ spatial resolution without sacrificing the local receptive field (LRF) for various image applications, specifically those that are sensitive to objects and features locations, using the definition of Fourier transform and the relation between spectral analysis and convolution kernels. The proposed method is then tested using a Monte Carlo simulation to evaluate its performance in spectral information coverage across images of various sizes, validating its ability to maintain coverage of a ratio of the spectral domain with a variation of around 20% of the desired coverage ratio. Finally, the AKL is validated for various image applications compared to other architectures such as Inception and VGG, demonstrating its capability to match Inception v4 in image classification applications, and outperforms it as images grow larger, up to a 30% increase in accuracy in object localization for the same number of parameters.

The ability to classify drones using radar signals is a problem of great interest. In this paper, we apply convolutional neural networks (CNNs) to the Short-Time Fourier Transform (STFT) spectrograms of the simulated radar signals reflected from the drones. The drones vary in many ways that impact the STFT spectrograms, including blade length and blade rotation rates. Some of these physical parameters are captured in the Martin and Mulgrew model which was used to produce the datasets. We examine the data under X-band and W-band radar simulation scenarios and show that a CNN approach leads to an F1 score of 0.816±0.011 when trained on data with a signal-to-noise ratio (SNR) of 10 dB. The neural network which was trained on data from an X-band radar with 2 kHz pulse repetition frequency was shown to perform better than the CNN trained on the aforementioned W-band radar. It remained robust to the drone blade pitch and its performance varied directly in a linear fashion with the SNR.

Detecting and identifying drones is of great interest due to the proliferation of highly manoeuverable drones with on-board sensors of increasing sensing capabilities. In this paper, we investigate the use of radars for tackling this problem. In particular, we focus on the problem of detecting rotary drones and distinguishing between single-propeller and multi-propeller drones using a micro-Doppler analysis. Two different radars were used, an ultra wideband (UWB) continuous wave (CW) C-band radar and an automotive frequency modulated continuous wave (FMCW) W-band radar, to collect micro-Doppler signatures of the drones. By taking a closer look at HElicopter Rotor Modulation (HERM) lines, the spool and chopping lines are identified for the first time in the context of drones to determine the number of propeller blades. Furthermore, a new multi-frequency analysis method using HERM lines is developed, which allows the detection of propeller rotation rates (spool and chopping frequencies) of single and multi-propeller drones. Therefore, the presented method is a promising technique to aid in the classification of drones.

A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering problem is provided in this paper. The practical utility of the path integral formula is demonstrated via some nontrivial examples. Specifically, it is shown that the simplest approximation of the path integral formula for the fundamental solution of the FPKfe can be applied to solve nonlinear continuous-discrete filtering problems quite accurately. The Dirac-Feynman path integral filtering algorithm is quite simple, and is suitable for real-time implementation.

An important problem in applied science is the continuous nonlinear filtering problem, i.e., the estimation of a Langevin state that is observed indirectly. In this paper, it is shown that Euclidean quantum mechanics is closely related to the continuous nonlinear filtering problem. The key is the configuration space Feynman path integral representation of the fundamental solution of a Fokker-Planck type of equation termed the Yau Equation of continuous-continuous filtering. A corollary is the equivalence between nonlinear filtering problem and a time-varying Schr¨odinger equation.